The uncertainty and the sensitivity of the response of a nonlinear stochastic multi-scale numerical model for randomly heterogenous material is investigated. 9 input parameters and 10 descriptors of the time-dependent output response are considered. The material model has been presented elsewhere and is introduced as a 'black box function' in the present paper, parameterized so that the model is deterministic and that variability in the outputs only comes from the variability introduced in the inputs. The objective is twofolds: (i) surveying the variety of macroscopic behaviors the material model considered is capable of representing, and (ii) assessing the relative importance of the model inputs in the model outputs to, for instance, define efficient parameters identification protocoles. A preliminary analysis of the linear dependency between the output descriptors is presented and a reduced set of 6 descriptors is eventually selected. Then, the influence of the model input parameters on each of these model response descriptors is investigated using a global sensitivity analysis technique based on the functional decomposition of their respective total variance.